Valid Mountain Array

Valid Mountain Array - Problem

Array Easy

Given an array of integers arr, return true if and only if it is a valid mountain array.

Recall that arr is a mountain array if and only if:

arr.length >= 3
There exists some i with 0 < i < arr.length - 1 such that:
- arr[0] < arr[1] < ... < arr[i - 1] < arr[i]
- arr[i] > arr[i + 1] > ... > arr[arr.length - 1]

This means the array must strictly increase to a peak, then strictly decrease.

Input & Output

Example 1 — Valid Mountain

$ Input: arr = [0,1,2,3,4,5,4,3,2,1,0]

› Output: true

💡 Note: This array strictly increases from 0 to 5, then strictly decreases from 5 to 0, forming a valid mountain with peak at index 5.

Example 2 — No Peak

$ Input: arr = [2,1]

› Output: false

💡 Note: Array length is less than 3, so cannot be a mountain. Also, it only decreases without any increase.

Example 3 — Only Increasing

$ Input: arr = [1,2,3,4,5]

› Output: false

💡 Note: Array only increases without any decreasing part. A mountain must have both uphill and downhill sections.

Constraints

1 ≤ arr.length ≤ 10⁴
0 ≤ arr[i] ≤ 10⁴

Visualization

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Asked in

G Google 15 a Amazon 12

The key insight is that a valid mountain must have exactly one peak with strict increases before and strict decreases after. Best approach is two pointers to walk up then down in one pass. Time: O(n), Space: O(1)

Common Approaches

✓ Brute Force - Check All Conditions

⏱️ Time: O(n) Space: O(1)

First check if length >= 3, then find the peak by scanning, then verify strict increasing before peak and strict decreasing after peak.

Two Pointers - Walk Up Then Down

⏱️ Time: O(n) Space: O(1)

Use one pointer to walk up the mountain from the start, then continue walking down from the peak. Check if we reached the end.

Brute Force - Check All Conditions — Algorithm Steps

Check if array length >= 3
Find the peak index by scanning
Verify strict increase before peak
Verify strict decrease after peak

Visualization

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Step-by-Step Walkthrough

Find Peak

Scan array to locate the single peak element

Check Uphill

Verify strict increasing before peak

Check Downhill

Verify strict decreasing after peak

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>

bool solution(int* arr, int size) {
    if (size < 3) {
        return false;
    }
    
    // Find peak
    int peak = -1;
    for (int i = 1; i < size - 1; i++) {
        if (arr[i] > arr[i-1] && arr[i] > arr[i+1]) {
            if (peak != -1) { // Multiple peaks
                return false;
            }
            peak = i;
        }
    }
    
    if (peak == -1) {
        return false;
    }
    
    // Check strict increasing before peak
    for (int i = 0; i < peak; i++) {
        if (arr[i] >= arr[i+1]) {
            return false;
        }
    }
    
    // Check strict decreasing after peak
    for (int i = peak; i < size - 1; i++) {
        if (arr[i] <= arr[i+1]) {
            return false;
        }
    }
    
    return true;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    
    int arr[1000];
    int size = 0;
    char* token = strtok(line, "[,]\n");
    
    while (token != NULL) {
        if (strlen(token) > 0 && token[0] != '[' && token[0] != ']') {
            arr[size++] = atoi(token);
        }
        token = strtok(NULL, "[,]\n");
    }
    
    bool result = solution(arr, size);
    printf(result ? "true\n" : "false\n");
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Multiple linear scans but still O(n) overall

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables

✓ Linear Space

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Medium Frequency

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force - Check All Conditions — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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